4.8 Bubble growth rate at different time ........................................................................... 66

4.9 The visualization result of bubble departure-nucleation process for heater #1 at 54C
............................................................................................................................... 69

mechanisms. Through this research, we would be able to achieve the following:

1. To find the basic physics of bubble coalescence and its effects on fluid

mechanics and heat transfer in the micro- and macro-layers and to develop a simple

mechanistic model for this phenomenon.

2. To obtain a fundamental understanding of the effects of heater length scale on

the boiling mechanism and boiling heat transfer.

We intend to study the detailed physics of bubble formation on small heaters,

bubble coalescence and bubble dynamics, and heat and mass transport during bubble

coalescence. The purpose is to delineate through experiment and analysis the

contributions of the key mechanisms to total heat transfer. This includes micro/macro

layer evaporation on single and merged bubbles attached to a heated wall, and heat

transfer enhancement during coalescence of bubbles on the heater wall. We intend to

provide answers to the following:

How will the bubble coalescence affect the heat transfer from the heater surface?

What mechanisms are at play during bubble coalescence? In other words, how do
the thermodynamic force, surface tension force, and hydrodynamic force that are
associated with the merging process balance one another?

What controls the bubble nucleation, growth, and departure from the heater
surface in nucleate boiling when bubble coalescence is part of the process?

How does the heater surface superheating level affect the bubble coalescence?

How does the heater length scale affect the bubble inception and boiling heat
transfer?

1.3 Significance and Justification

Nucleate boiling has been recognized as one of the most efficient heat transfer

mechanisms. In many engineering applications, nucleate boiling heat transfer is the mode

of choice. Boiling heat transfer has the potential advantage of being able to transfer a

large amount of energy over a relatively narrow temperature range with a small weight to

power ratio. For example, boiling heat transfer has been widely used in microelectronics

cooling.

Apart from the engineering importance, there are science issues. Currently, the

mystery of critical heat flux remains unsolved. As a matter of fact controversies over the

basic transport mechanisms of bubble coalescence and its effects on the role of

the computer is used to select the heaters and set their temperature through D/A card and

acquire data through A/D cards.

3.4 Experiment Procedure

3.4.1 Heater Calibration

3.4.1.1 Calibration apparatus

The calibration apparatus includes the constant temperature oil tank with oil-

circulating pump and temperature control system, as shown in figure 3.4. The constant oil

tank functions to impinge the constant oil into the heater array surface. The temperature

on I-
Dfl--- Decodei

Digital camera
for bottom view

Figure 3.3 Boiling apparatus.

control system is used to keep the circulating oil at a constant temperature. Calibration is

the beginning of the experiment, and it is also a very important step since the following

boiling experiment will be based on the calibration data. Therefore, much more care

should be exercised to ensure the accuracy.

3.4.1.2 Calibration procedure

The calibration procedure is as follows:

1. Set the temperature controller at a certain temperature.

2. Circulating the fluids in the calibration tank. Power the heating components.
After this, several minutes or more are needed to maintain the temperature of the
circulating fluid at the stable temperature.

3. Start the calibration routine in PC and calibrate. The computer automatically
saves the calibration result.

Lubricate Oil

Insulation

(b)

Figure 3.4 Schematic of calibration apparatus and temperature control loop. (a) The
calibration system; (b) The electrical loop to maintain the temperature of calibration oil.

4. Set the heater array at another temperature. Follow the first and second steps till
all calibration is completed.

However, by powering two heaters that are too far apart such as #1 and #25, two single

bubbles will be generated, but the bubble departure sizes are not large enough for them to

touch and merge before they depart. Therefore, for coalescence to take place, the active

heaters have to be close enough within a certain range. The power consumed by the

heater was acquired by the computer data acquisition system (figure 3.3). Data were

acquired at a sampling rate of 40,000 Hz for each channel of the A/D system, after

allowing the heater to remain at a set temperature for 15 minutes. The data were found to

be repeatable under these conditions. The acquired data were converted to heat flux from

the heater according to the following basic relationship:

q" = (V2 /R) I/A (3.2)

For each heater configuration, the heaters were always set at the same temperature

for the bubble coalescence experiment, and this temperature is varied to investigate the

effect of heater superheat on the bubble coalescence. For all cases, the dissipation from

heaters was acquired in sequence. Because steady state has been reached in all these

experiments, sequential data acquisition does not affect the data accuracy. The bubble

visualization includes both bottom and side views; though bottom views are more

suitable for multiple bubble coalescence. The semi-transparent nature of the heater

substrate made it possible to take images from below the heater. The setup of experiment

has been shown in figure 3.3. A high-speed digital camera (MotionScope PCI 8000S) was

used to take images at 2000 fps with a resolution of 240 x 210, with maximum 8 seconds

of recording time. The bubble visualization was performed using the shadowgraph

technique. In this technique, the bubbles were illuminated from one side while the images

were taken from the other side.

3.5 Heat Transfer Analysis and Data Reduction

3.5.1 Qualitative Heat Transfer Analysis

Each heater has a dimension of 0.27mm x 0.27mm. For such a small heater, the

heat transfer behavior is hardly similar to that for large heaters. Specifically, the edge

effects greatly affect the heat transfer. Since the heaters used in our experiment are

always kept at a constant temperature, the data reduction turns out to be much simpler.

Qualitatively, the heat dissipated from the heater at a certain temperature, by reference to

figure 3.7(a), is composed of the following components:

1. Boiling heat transfer from the heater in boiling experiment, when the heater is
superheated high enough.

2. Conduction to the substrate on which the heater is fabricated. This is due to the
temperature gradient between the heater and the ambient through the substrate.

3. Radiation heat transfer due to the temperature difference between the heater
and ambient.

4. Natural convection between the heater and air and FC-72 vapor mixture when
the heater array is positioned vertically to be separated from the liquid for data reduction

experiment. This natural convection is replaced by the boiling heat transfer from the
heater when the boiling occurs on the heater surface.

3.5.2 Data Reduction Procedure

To obtain the heat transfer rates due to boiling only, we conduct the experiments

by the following procedure:

1. Measure the total heat flux supplied to the heater during the boiling process at

different heater temperatures.

The total heat flux with boiling:

q"rawl = q"top + q"condl + q"radl. (3.3)

2. Tilt the boiling chamber 90, so that the heater is exposed to the air and FC-72

vapor, while separated from FC-72 liquid, and measure the total heat flux without boiling

at corresponding temperatures.

Therefore, the total heat flux without boiling:

q'raw2 = q"natural + q"cond2 + q"rad2 (3.4)

The q"condl in Eq.(3.3) and q"cond2 in Eq.(3.4) are the conduction to the substrate

and ambient through the substrate. Because the heater is held at a constant temperature,

they are independent of the state of fluid above the heater, thus we assume q"condji=q"cond2.

The same reasoning also goes with radiation. Thus, from Eq.(3.3) and Eq.(3.4) the heat

dissipated above the heater during boiling can be derived as the following:

q"top = q"rawl q"raw2 + q"natural (3.5)

where q"naturai is the contribution from natural convection with the mixture of air and FC-

72 vapor. To get a good estimate of the natural convection component in Eq.(3.5), we

need to pay special attention to the small size of the heater we used. The details for this

estimation are given in the following.

Bulk liquid

Ambient room
(a)

q a

SMixture of air
and vapor
^^^^^Bk ^(flnaftur

Ambient room 'aui

q'&nd2 4.
q'rd2

(b)

Figure 3.7 The schematic showing the heat dissipation from a heater. (a) The heat transfer
paths from the microheater during boiling experiment; (b) The heat transfer paths from
the heater during data reduction experiment.

3.5.3 Determination of Natural Convection on the Microheaters

We have done a significant amount of literature research in order to rationally

determine the natural convection on the heaters we were using. We first use the empirical

correlations to evaluate the heat dissipated from the heater, in which we use the results of

Ostrach (1953) to calculate this natural convection. Then the calculated heat dissipation is

used to compare with experimental results.

Conduction. We assume one dimensional conduction from the heater to the

ambient through the quartz substrate. The ambient has a constant temperature of 25C0(2.

Conductivity of the quartz substrate is ksub = 1.5 w/mK. For different heater temperatures

To, using Fourier law of conduction, we calculate the conduction heat flux. For

simplicity, we neglected the epoxy thickness that is used to seal the heater at the bottom.

Since we calculate the conduction based on quartz substrate only, neglecting the heat

transfer resistance of epoxy, the calculated conduction heat transfer should be larger than

that if the epoxy layer is accounted for.

Convection. When the liquid was separated from the heater, there is natural

convection heat transfer to the mixture of air and vapor from the heater. For this

calculation, the mixture of FC-72 vapor and air is approximated as ideal gas of air.

Radiation. With the approximation of black body, the radiation heat flux is

calculated as follows:

q"= ( T,4- To4) (3.6)

where cr is the Stefan-Boltzmann constant.

The calculation results for the above heat transfer modes have been shown in

figure (3.8). From this figure, obviously, the sum of convection, conduction and

Figure 3.11 The uncertainty at different temperatures. (a) The uncertainty for single
bubble boiling at different temperatures; (b) The uncertainty for dual-bubble coalescence
together with single bubble boiling.

coalescence, the overall boiling heat transfer has been increased. (2) due to heater

interaction, the natural convection is smaller for the single heater case.

In summary, for temperatures, the oil temperature fluctuation during calibration

contributes to the main uncertainty, though opamp offset also has some contributions.

Natural convection is the main contributor to the boiling heat transfer uncertainty. The

overall uncertainty for heater temperature is estimated about 0.7C, and the overall

uncertainty of boiling heat flux is about 15% between 100C ~ 170C, and this

uncertainty is temperature dependent. The uncertainty of dual bubble boiling is smaller

than that of the single bubble boiling due to coalescence-enhanced heat transfer.

CHAPTER 4
SINGLE BUBBLE BOILING EXPERIMENT

4.1 Introduction

Applications of microtechnology must utilize components or systems with

microscale fluid flow, heat and mass transfer. As the size of individual component